Abstract
There are numerous priority deriving methods (PDMs) for pairwise-comparison-based (PCB) problems. They are often examined within the Analytic Hierarchy Process (AHP), which applies the Principal Right Eigenvalue Method (PREV) in the process of prioritizing alternatives. It is known that when decision makers (DMs) are consistent with their preferences when making evaluations concerning various decision options, all available PDMs result in the same priority vector (PV). However, when the evaluations of DMs are inconsistent and their preferences concerning alternative solutions to a particular problem are not transitive (cardinally), the outcomes are often different. This research study examines selected PDMs in relation to their ranking credibility, which is assessed by relevant statistical measures. These measures determine the approximation quality of the selected PDMs. The examined estimates refer to the inconsistency of various Pairwise Comparison Matrices (PCMs)—i.e., W = (wij), wij > 0, where i, j = 1,…, n—which are obtained during the pairwise comparison simulation process examined with the application of Wolfram’s Mathematica Software. Thus, theoretical considerations are accompanied by Monte Carlo simulations that apply various scenarios for the PCM perturbation process and are designed for hypothetical three-level AHP frameworks. The examination results show the similarities and discrepancies among the examined PDMs from the perspective of their quality, which enriches the state of knowledge about the examined PCB prioritization methodology and provides further prospective opportunities.
Highlights
The method of creating a ranking based on pairwise comparisons of alternatives was already known in the Middle Ages
The possibility was created for a decision makers (DMs) to assess the risk of accepting an ineffective priority deriving methods (PDMs) or rejecting an effective PDM—the standard problem known to every statistician and very important to each DM during the statistical evaluation of decisional options; i.e., statistical alternative hypothesis testing
Discrepancies and similarities among examined PDMs have been examined in this research paper from various perspectives, including the statistical approach
Summary
The method of creating a ranking based on pairwise comparisons of alternatives was already known in the Middle Ages. Alternatives began to be compared quantitatively, which was initially connected with the need to compare psychophysical stimuli [3,4]. This path was later developed [5] and used in various forms for different objectives, including economics [6], consumer research, psychometrics, health care and others. Thanks to Saaty and his seminal paper [7] in which he defined the Analytic Hierarchy Process (AHP), comparing alternatives in a pairwise mode began to be considered basically as a multi-criteria decision-making method. Numerous studies have presented scientific evidence of the fundamental flows of the AHP; see, e.g., [12,13,14,15]
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